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Seven Divisibility Settlement (Posted on 2010-11-13) Difficulty: 3 of 5
M is a positive integer ≥ 2 such that 3M + 4M is divisible by M.

Is M always divisible by 7?

If so, prove it. Otherwise, provide a counterexample.

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (2 votes)

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re(2): Possible Solution Comment 3 of 3 |
(In reply to re: Possible Solution by Brian Smith)

My workings are long gone, but there is an additional note in my notebook that 3M + 4 = (3+4)(other factors) if M is odd, as it must be.

My concern at that point seems to have been eliminating a 7-free M as a divisor of the (other factors) hence the digression into Fermat.

  Posted by broll on 2017-06-24 23:37:45
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